- Email: [email protected]
Single electron capture measurements in collisions of K+ on N2
Nuclear Instruments and Methods in Physics Research B xxx (2014) xxx–xxx
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Single electron capture measurements in collisions of K+ on N2 F.B. Alarcón a, B.E. Fuentes b,⇑, H. Martínez a, F.B. Yousif c a
Laboratorio de Espectroscopia, Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, 62210 Cuernavaca, Morelos, Mexico Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, 04510 México D.F., Mexico c Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad #1000, Col. Chamilpa, C.P. 62210, Cuernavaca, Morelos, Mexico b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Single electron capture Cross section Ion beam experiment Potassium N2
a b s t r a c t Absolute total charge transfer cross sections have been measured for K+–N2 collisions, at impact energies between 1.0 and 3.5 keV. The charge transfer cross sections show a monotonic increasing behaviour as a function of the incident energy. Agreement with other groups is observed as the present measurements extend to lower energies. A semi-empirical calculation shows a similar behaviour to the present data with respect to the electron capture cross sections as a function of energy. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction The present work is a continuation to our previous work on electron capture for the processes of K+ collisions with H2 [1] and CH4 [2]. Ion beam spectroscopy method was applied in the energy range of 1.0–3.5 keV in the present investigation. The research work related to ion–molecule interaction which is important for fundamental as well as for applied fields [3–6] such as surface physics and beam deposition [7]. Equally in planetary atmospheric science, singly ionized potassium has been detected in Io’s atmosphere. Gochitashvili et al. [8] measured the cross sections for K+ collisions with N2 in the energy range 1–3 keV employing both optical and collision spectroscopy. In addition, Ogurtsov et al. [9] measured the same cross section within the energy range of 6–20 keV employing ion beam spectroscopy method taking into account the possible neutrals scattering at low energy. Equally the same cross section was measured by Lo and Fite [10] between 12 and 1200 keV. The serious discontinuity between the measurements of Gochitashvili et al. [8] (1–3 keV) and those of Ogurtsov et al. [9] (6–20 keV) is the motivation for the present measurements taking into account the importance of the low energy scattering. 2. Experimental method Schematic of the experimental setup is shown in Fig. 1. The experimental apparatus and procedure are outlined in our previous ⇑ Corresponding author. Address: Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Departamento de Fisica Circuito Exterior s/n, Ciudad Universitaria, 04510 Coyoacan, Mexico D.F., Mexico. Tel.: +52 55 56224842. E-mail address: [email protected] (B.E. Fuentes).
publications [1,2,11]. A brief description of its most important characteristics is presented here. Surface ionization of KCl vapors on a hot tungsten surface was performed resulting in the formation of Potassium ions, with only a narrow energy spread (60.3 eV). All ions are in the ground electronic state. As impurity ions involved in the beam are less than 0.1% of that of K+ ions, a fact that have been confirmed employing a mass spectrometer that is separately integrated in our laboratory, therefore mass separation in situ was not employed,. After acceleration to the desired energy (1.0–3.5 keV), the K+ is allowed to pass through several knife edged collimating apertures. Following that, ions entered the target cell that consisted of a cylindrical cell of 2.5 cm of diameter and length, with 1 mm entrance aperture and a 2 mm wide along with 6 mm long exit aperture. The target cell was filled with N2 gas of 99.99% purity. The angular spread of the primary ion beam is estimated to be less than 0.4° in the collision chamber. Following the target region, neutral and charged particles were separated electrostatically. A Faraday cup and a secondary emission detector were employed for the detection of neutral and charged components. Beam profiles were obtained by scanning the charged beam across the Faraday cup from which a well resolved plateau was demonstrated verifying total collection. Ion beams intensities were observed to be very stable during experimental measurements. The target gas pressure was directly measured with a MKS Baratron Capacitance manometer. The single electron capture cross sections r10 were obtained from thin-target data. To a good approximation the cross-section is the slope of the linear growth of the beam component curve (GR method):
r¼
dF : dp
ð1Þ
http://dx.doi.org/10.1016/j.nimb.2014.02.086 0168-583X/Ó 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: F.B. Alarcón et al., Single electron capture measurements in collisions of K+ on N2, Nucl. Instr. Meth. B (2014), http:// dx.doi.org/10.1016/j.nimb.2014.02.086
2
F.B. Alarcón et al. / Nuclear Instruments and Methods in Physics Research B xxx (2014) xxx–xxx
Fig. 1. Schematic diagram of the experimental apparatus.
where F is the observed neutral fractional yield (F = I0/I+), I0 is the neutral current, I+ is the projectile beam current, and p the target thickness. The p was derived from the ideal gas equation:
K0
ð2Þ
where P is the pressure in the gas cell, ‘ is its effective length, T is the temperature, and k is Boltzmann’s constant. The background pressure in the vacuum chamber was 1.0 106 Torr and the maximum operating pressure with beam and target gas load on was 9.0 106 Torr. An important consideration in low-energy absolute cross-section measurements is to ensure complete collection of the scattered beam. This was experimentally verified by measuring the electron capture of protons in collisions with Ar at 1.5 keV. We found r10 = 11.9 Å2. This result agrees very well to that measured by Johnson et al. [12] with the value of r10 = 11.0 Å2. The Faraday cup was designed to ensure complete electrostatic suppression of secondary electrons. Typical suppression voltages of 200 V were applied and a plateau in the signal was clearly evident. Complete care had to be taken to ensure that projectile beam current (I+) and neutral current (I0) were measured with the same efficiency. The above mentioned procedure introduced uncertainties in the r10 cross section. First, errors concerning the measured fractions were estimated from the reproducibility of the data. Second, errors due to the determination of beam intensity were evaluated by the uncertainties encountered in obtaining the slope. This uncertainty was estimated to be less than 10%. Other sources of error, such as the measured target gas pressures and deviations from the thin target conditions, have been considered. The estimated root mean square error is 15%, whereas the total cross sections were reproducible to within 15% from day to day. 3. Results and discussion Fig. 2 shows typical growth-rate curves obtained at energies of 1.0, 2.0 and 3.0 keV for the K+–N2 processes, where single collision conditions are evident and single electron capture cross sections r was obtained from thin-target data. To a good approximation the cross-section is the slope of the linear growth of the beam component curve (growth-rate method, see Eq. (1). The background pressure in the vacuum system was 1.0 106 Torr. Several sources of systematic errors are present in the r10 cross section. First, errors concerning the measured fractions were estimated from the reproducibility of the data. Second, errors due to the determination of the beam intensity were evaluated by the uncertainties encountered in obtaining the slope of Fig. 2. This was estimated to be less than 10%. The effective path length is longer than the physical path length due to gas streaming from the apertures as a result of differential pumping. This effective increase in path length was estimated to be approximately 3%. That increase was noted from a comparison
0.3
2.0 keV
-3
‘P kT
0.4
F10 (x10 )
p¼
3.0 keV
K+ + N2
0.2
X0.5 x0.1
0.1
1.0 keV
0.0 0
2
4
6
8 13
10
12
14
-2
π(10 cm ) Fig. 2. Growth-rate curves of K0 produced by electron capture of K+ on N2 with line fit at 1, 2 and 3 keV.
of the measured cross sections and by a simple calculation based on isotropic-molecular flow of gas from the apertures. The uncertainty associated with a length is estimated to be less than ±2%. We estimate the total uncertainty to be less than ±15%. This estimate accounts for both random and systematic errors. Our present measured data charge capture cross sections for the K+–N2 reaction for the 1–3 keV collision range are shown in Fig. 3, together with those of Gochitashvili et al. [8] (1–3 keV), Ogurtsov et al. [9] (6–20 keV), and Lo and Fite [10] (12 and 1200 keV). There is a remarkable continuity of our data and those of Ogurtsov et al. [9], and Lo and Fite [10]. While a disagreement is apparent between the present data and the data of Gochitashvili et al. [8], considering the fact that our previous measurements on K+–H2 were found to reasonably agree with those of Gochitashvili et al. [13]. However it is rather difficult to attempt identifying the reasons of this discrepancy in the above mentioned data. Yet, it is imperative to point out to a certain concerns regarding the methods and measurements of Ref. [8]. The data presented in [8] included measurements for the electron capture of K+ ions with N2, mostly focused on dissociative excitation by observing the KI (766.5 nm) emission line. The charge transfer process leading to the excited K(4p) state was concluded [8] to be the only channel. This would imply that both the electron capture and excitation cross sections would show similar behavior and trend as a function of energy. In Ref. [8], the KI (766.5 nm) emission line reaches a maximum at 6 keV collision energy and maintain that value up to 10 keV. While their measured electron capture cross section shows a rapid increase up to an energy of 3 keV. The limited energy range of the
Please cite this article in press as: F.B. Alarcón et al., Single electron capture measurements in collisions of K+ on N2, Nucl. Instr. Meth. B (2014), http:// dx.doi.org/10.1016/j.nimb.2014.02.086
F.B. Alarcón et al. / Nuclear Instruments and Methods in Physics Research B xxx (2014) xxx–xxx
3
The quantity k is given by:
n o v ½1 V 11 ðRc Þ=E0 1=2 V 011 ðRc Þ V 022 ðRc Þ k ¼ 2pH212 = h
1
-16
0.1 +
σ10 (10
K + N2
0
K
Ogurtsov et al Lo and Fite Gochitashvili et al Olson model Present data
0.01
H12 ¼
1E-3 1
10
100
1000
Energy (keV) Fig. 3. Total electron-capture cross section for K+–N2 collisions.
electron capture does not permit compression between the two measurements as far as the behaviour of excitation and charge transfer cross section as they should in principal show the same trend. However, measurements were made for the excitation function of the resonance emission line of 766.5 nm in collisions between potassium ions and N2 molecules [14] employing the same technique described in [8]. Their measurements [14] between 0.5 and 10 keV collisional energy for the KI (766.5 nm) emission line shows a clear maximum between 6 and 8 keV energy followed by a slow decreasing trend as it reaches 10 keV, while the same measurements in [8] shows that the emission line KI (766.5 nm) increases as the energy increases up to 6 keV and remain virtually constant as the collision energy increases to 10 keV. No explanation was offered regarding this difference in the 2001 publication [8]. On the other hand, considering our measured capture cross sections together with the data of [9,10] indicate a maximum between 20 and 50 keV collisional energy compared to the 6 keV maximum reported in [14]. Moreover, the excitation cross section reported by [14] for the K+–N2 processes is about a factor of three higher than that for K+–H2 from which they concluded that the excitation cross section is proportional to the energy defect of the colliding partners in the case of molecular targets. Yet this is in contrast to the data of [15–17] reported within [10], in which the reported capture cross section for K+–O2 (DE = 7.73 eV) is higher than that for K+–N2 (DE = 12.9 eV). While our present electron capture cross section of K+–N2 is about a factor of two lower than that for K+–H2, a behaviour that is confirmed by the data of [15–17] on K+ on N2 and O2 and reported within [10]. As a result, there is a need for further theoretical and experimental data regarding the above mentioned process in order to establish a reliable data for the K+–N2 collision system. However it is possible to evaluate the behaviour of the charge transfer cross section using the semiempirical model of Olson [18,19] for the system:
Kþ ð1 S0 Þ þ N2 ! K0 ð4s2 S1=2 Þ þ Nþ2 11:238 eV; The total single-electron-capture cross sections are calculated by the relation [18,19]:
r ¼ 4pR2c ½1 V 11 ðRc Þ=E0
Z 1
1
expðkxÞ½1 expðkxÞx3 dx
ð4Þ
V 022
where and are the first derivatives of the potentials V11 and V22 at Rc. The incident velocity is given by v0 and E0 is the incident energy. Rc is interpreted as the internuclear separation at which charge transfer occurs. Since, V11(Rc) is of the order of eV and the incident energy E0 of the order of keV, we can estimated ½1 V 11 ðRc Þ=E0 1. The coupling matrix element H12 was calculated through the relation:
2
cm )
V 011
ð3Þ
1 acR expð0:86R Þ 2
ð5Þ
where R ¼ 12 ðða þ cÞRc Þ. We used 12 a2 ¼ 15:58 eV as the effective ionization potential of the N2 target and 12 c2 ¼ 4:341 eV as the Kground-state electron affinity. H12 was found to be equal to 1.59 eV. While, Rc = 2.20a0, and jDV ; ðRc Þj ¼ 5:91 eV=a0 were fitted until the maximum cross section value corresponding to an energy Emax predicted by the Massey adiabatic model (evaluated using the energy defect |DE| as the only parameter) was obtained. The estimated electron transfer cross sections are shown in Fig. 3 as a solid line. The calculated r is seen to agree in behaviour with the present experimental data in the present energy range as well as with those of Gochitashvili et al. [8], Ogurtsov et al. [9], and Lo and Fite [10]. 4. Conclusions Absolute total electron transfer cross sections have been measured for the K+–N2 system, at impact energies between 1.0 and 3.5 keV. The charge transfer cross sections show a monotonic increasing behaviour as a function of the incident energy. Our present experimental data show continuity with the results of Ogurtsov et al. [9] which in turn show a reasonable overlap with the data reported by Lo and Fite [10] at higher energies. Our present electron capture cross sections as well as our previous data on K+–H2 increases as the energy defect decreases taking in agreement with the results of Lo and Fite [10] and Layton and Fite [17], while in disagreement with the data of Gochitashvili et al. [8]. The calculation of r employing the semi empirical model of Olson is seen to agree in behaviour with the present experimental data in the present energy range as well as well as with those of other groups. Agreement and disagreement with other groups points to the need for further theoretical and experimental data employing different methods regarding the above mentioned process in order to establish a reliable data for the K+–N2 collision system. Acknowledgments The authors are grateful to O. Flores, F. Castillo and José Rangel for technical assistance. This research was partially sponsored by DGAPA IN-109511 and CONACyT 128714. References [1] [2] [3] [4]
F.B. Alarcón, H. Martínez, B.E. Fuentes, F.B. Yousif, Phys. Scr. 88 (2013) 025304. F.B. Alarcón, H. Martínez, Nucl. Instrum. Meth. B 299 (2013) 29. R.E. Johnson, Icarus 143 (2000) 429. T.W. Hartquist, S.A.E.G. Falle, D.A. Williams, Astrophys. Space Sci. 288 (2003) 369. [5] A. Burrows, W.B. Hubbard, J.I. Lunine, J. Liebert, Rev. Mod. Phys. 73 (2001) 719. [6] D. Sudarsky, A. Burrows, P. Pinto, Astrophys. J. 538 (2000) 885. [7] F.M. Bieniosek, L.R. Prost, P.A. Seidl, A.W. Molvik, M. Kireeff Covo, Phys. Rev. Spec. Top. Accelerators Beam 10 (2007) 93201.
Please cite this article in press as: F.B. Alarcón et al., Single electron capture measurements in collisions of K+ on N2, Nucl. Instr. Meth. B (2014), http:// dx.doi.org/10.1016/j.nimb.2014.02.086
4 [8] [9] [10] [11]
F.B. Alarcón et al. / Nuclear Instruments and Methods in Physics Research B xxx (2014) xxx–xxx
M. Gochitashvili, B. Kikiani, R. Lomsadze, Hyperfine Interact. 132 (2001) 517. G.N. Ogurtsov, B.I. Kikiani, I.P. Flaks, Sov. Phys. 11 (1966) 362. H.H. Lo, W.L. Fite, Atomic Data 1 (1970) 305–328. F.B. Yousif, B.E. Fuentes, H. Martínez, J. Phys. B At. Mol. Opt. Phys. 43 (2010) 235206. [12] L.K. Johnson, R.S. Gao, C.L. Hakes, K.A. Smith, R.F. Stebbings, Phys. Rev. A 40 (1989) 4920. [13] M. Gochitashvili, B. Kikiani, R. Lomsadza, Hyperfine Interact. 132 (2001) 517.
[14] B.I. Kikiani, M.R. Gochitashvili, R.V. Kvizhinadze, V.A. Ankudinov, Zh. Eksp. Teor. Fiz. 87 (1984) 1906. [15] W.L. Fite, J.K. Layton, R.F. Stebbings, N.M. AFWL-TR-65-181, 1966 (Feb). [16] J.K. Layton et al., Phys. Rev. 161 (1967) 73. [17] J.K. Layton, W.L. Fite, N.M. AFWL-TR-67-2, 1967 (May). [18] R.E. Olson, F.T. Smith, E. Bauer, Appl. Opt. 10 (1971) 1848. [19] R.E. Olson, Phys. Rev. A 2 (1970) 121.
Please cite this article in press as: F.B. Alarcón et al., Single electron capture measurements in collisions of K+ on N2, Nucl. Instr. Meth. B (2014), http:// dx.doi.org/10.1016/j.nimb.2014.02.086
Contents lists available at ScienceDirect
Nuclear Instruments and Methods in Physics Research B journal homepage: www.elsevier.com/locate/nimb
Single electron capture measurements in collisions of K+ on N2 F.B. Alarcón a, B.E. Fuentes b,⇑, H. Martínez a, F.B. Yousif c a
Laboratorio de Espectroscopia, Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México, Apartado Postal 48-3, 62210 Cuernavaca, Morelos, Mexico Facultad de Ciencias, Universidad Nacional Autónoma de México, Circuito Exterior, Cd. Universitaria, 04510 México D.F., Mexico c Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad #1000, Col. Chamilpa, C.P. 62210, Cuernavaca, Morelos, Mexico b
a r t i c l e
i n f o
Article history: Available online xxxx Keywords: Single electron capture Cross section Ion beam experiment Potassium N2
a b s t r a c t Absolute total charge transfer cross sections have been measured for K+–N2 collisions, at impact energies between 1.0 and 3.5 keV. The charge transfer cross sections show a monotonic increasing behaviour as a function of the incident energy. Agreement with other groups is observed as the present measurements extend to lower energies. A semi-empirical calculation shows a similar behaviour to the present data with respect to the electron capture cross sections as a function of energy. Ó 2014 Elsevier B.V. All rights reserved.
1. Introduction The present work is a continuation to our previous work on electron capture for the processes of K+ collisions with H2 [1] and CH4 [2]. Ion beam spectroscopy method was applied in the energy range of 1.0–3.5 keV in the present investigation. The research work related to ion–molecule interaction which is important for fundamental as well as for applied fields [3–6] such as surface physics and beam deposition [7]. Equally in planetary atmospheric science, singly ionized potassium has been detected in Io’s atmosphere. Gochitashvili et al. [8] measured the cross sections for K+ collisions with N2 in the energy range 1–3 keV employing both optical and collision spectroscopy. In addition, Ogurtsov et al. [9] measured the same cross section within the energy range of 6–20 keV employing ion beam spectroscopy method taking into account the possible neutrals scattering at low energy. Equally the same cross section was measured by Lo and Fite [10] between 12 and 1200 keV. The serious discontinuity between the measurements of Gochitashvili et al. [8] (1–3 keV) and those of Ogurtsov et al. [9] (6–20 keV) is the motivation for the present measurements taking into account the importance of the low energy scattering. 2. Experimental method Schematic of the experimental setup is shown in Fig. 1. The experimental apparatus and procedure are outlined in our previous ⇑ Corresponding author. Address: Facultad de Ciencias, Universidad Nacional Autonoma de Mexico, Departamento de Fisica Circuito Exterior s/n, Ciudad Universitaria, 04510 Coyoacan, Mexico D.F., Mexico. Tel.: +52 55 56224842. E-mail address: [email protected] (B.E. Fuentes).
publications [1,2,11]. A brief description of its most important characteristics is presented here. Surface ionization of KCl vapors on a hot tungsten surface was performed resulting in the formation of Potassium ions, with only a narrow energy spread (60.3 eV). All ions are in the ground electronic state. As impurity ions involved in the beam are less than 0.1% of that of K+ ions, a fact that have been confirmed employing a mass spectrometer that is separately integrated in our laboratory, therefore mass separation in situ was not employed,. After acceleration to the desired energy (1.0–3.5 keV), the K+ is allowed to pass through several knife edged collimating apertures. Following that, ions entered the target cell that consisted of a cylindrical cell of 2.5 cm of diameter and length, with 1 mm entrance aperture and a 2 mm wide along with 6 mm long exit aperture. The target cell was filled with N2 gas of 99.99% purity. The angular spread of the primary ion beam is estimated to be less than 0.4° in the collision chamber. Following the target region, neutral and charged particles were separated electrostatically. A Faraday cup and a secondary emission detector were employed for the detection of neutral and charged components. Beam profiles were obtained by scanning the charged beam across the Faraday cup from which a well resolved plateau was demonstrated verifying total collection. Ion beams intensities were observed to be very stable during experimental measurements. The target gas pressure was directly measured with a MKS Baratron Capacitance manometer. The single electron capture cross sections r10 were obtained from thin-target data. To a good approximation the cross-section is the slope of the linear growth of the beam component curve (GR method):
r¼
dF : dp
ð1Þ
http://dx.doi.org/10.1016/j.nimb.2014.02.086 0168-583X/Ó 2014 Elsevier B.V. All rights reserved.
Please cite this article in press as: F.B. Alarcón et al., Single electron capture measurements in collisions of K+ on N2, Nucl. Instr. Meth. B (2014), http:// dx.doi.org/10.1016/j.nimb.2014.02.086
2
F.B. Alarcón et al. / Nuclear Instruments and Methods in Physics Research B xxx (2014) xxx–xxx
Fig. 1. Schematic diagram of the experimental apparatus.
where F is the observed neutral fractional yield (F = I0/I+), I0 is the neutral current, I+ is the projectile beam current, and p the target thickness. The p was derived from the ideal gas equation:
K0
ð2Þ
where P is the pressure in the gas cell, ‘ is its effective length, T is the temperature, and k is Boltzmann’s constant. The background pressure in the vacuum chamber was 1.0 106 Torr and the maximum operating pressure with beam and target gas load on was 9.0 106 Torr. An important consideration in low-energy absolute cross-section measurements is to ensure complete collection of the scattered beam. This was experimentally verified by measuring the electron capture of protons in collisions with Ar at 1.5 keV. We found r10 = 11.9 Å2. This result agrees very well to that measured by Johnson et al. [12] with the value of r10 = 11.0 Å2. The Faraday cup was designed to ensure complete electrostatic suppression of secondary electrons. Typical suppression voltages of 200 V were applied and a plateau in the signal was clearly evident. Complete care had to be taken to ensure that projectile beam current (I+) and neutral current (I0) were measured with the same efficiency. The above mentioned procedure introduced uncertainties in the r10 cross section. First, errors concerning the measured fractions were estimated from the reproducibility of the data. Second, errors due to the determination of beam intensity were evaluated by the uncertainties encountered in obtaining the slope. This uncertainty was estimated to be less than 10%. Other sources of error, such as the measured target gas pressures and deviations from the thin target conditions, have been considered. The estimated root mean square error is 15%, whereas the total cross sections were reproducible to within 15% from day to day. 3. Results and discussion Fig. 2 shows typical growth-rate curves obtained at energies of 1.0, 2.0 and 3.0 keV for the K+–N2 processes, where single collision conditions are evident and single electron capture cross sections r was obtained from thin-target data. To a good approximation the cross-section is the slope of the linear growth of the beam component curve (growth-rate method, see Eq. (1). The background pressure in the vacuum system was 1.0 106 Torr. Several sources of systematic errors are present in the r10 cross section. First, errors concerning the measured fractions were estimated from the reproducibility of the data. Second, errors due to the determination of the beam intensity were evaluated by the uncertainties encountered in obtaining the slope of Fig. 2. This was estimated to be less than 10%. The effective path length is longer than the physical path length due to gas streaming from the apertures as a result of differential pumping. This effective increase in path length was estimated to be approximately 3%. That increase was noted from a comparison
0.3
2.0 keV
-3
‘P kT
0.4
F10 (x10 )
p¼
3.0 keV
K+ + N2
0.2
X0.5 x0.1
0.1
1.0 keV
0.0 0
2
4
6
8 13
10
12
14
-2
π(10 cm ) Fig. 2. Growth-rate curves of K0 produced by electron capture of K+ on N2 with line fit at 1, 2 and 3 keV.
of the measured cross sections and by a simple calculation based on isotropic-molecular flow of gas from the apertures. The uncertainty associated with a length is estimated to be less than ±2%. We estimate the total uncertainty to be less than ±15%. This estimate accounts for both random and systematic errors. Our present measured data charge capture cross sections for the K+–N2 reaction for the 1–3 keV collision range are shown in Fig. 3, together with those of Gochitashvili et al. [8] (1–3 keV), Ogurtsov et al. [9] (6–20 keV), and Lo and Fite [10] (12 and 1200 keV). There is a remarkable continuity of our data and those of Ogurtsov et al. [9], and Lo and Fite [10]. While a disagreement is apparent between the present data and the data of Gochitashvili et al. [8], considering the fact that our previous measurements on K+–H2 were found to reasonably agree with those of Gochitashvili et al. [13]. However it is rather difficult to attempt identifying the reasons of this discrepancy in the above mentioned data. Yet, it is imperative to point out to a certain concerns regarding the methods and measurements of Ref. [8]. The data presented in [8] included measurements for the electron capture of K+ ions with N2, mostly focused on dissociative excitation by observing the KI (766.5 nm) emission line. The charge transfer process leading to the excited K(4p) state was concluded [8] to be the only channel. This would imply that both the electron capture and excitation cross sections would show similar behavior and trend as a function of energy. In Ref. [8], the KI (766.5 nm) emission line reaches a maximum at 6 keV collision energy and maintain that value up to 10 keV. While their measured electron capture cross section shows a rapid increase up to an energy of 3 keV. The limited energy range of the
Please cite this article in press as: F.B. Alarcón et al., Single electron capture measurements in collisions of K+ on N2, Nucl. Instr. Meth. B (2014), http:// dx.doi.org/10.1016/j.nimb.2014.02.086
F.B. Alarcón et al. / Nuclear Instruments and Methods in Physics Research B xxx (2014) xxx–xxx
3
The quantity k is given by:
n o v ½1 V 11 ðRc Þ=E0 1=2 V 011 ðRc Þ V 022 ðRc Þ k ¼ 2pH212 = h
1
-16
0.1 +
σ10 (10
K + N2
0
K
Ogurtsov et al Lo and Fite Gochitashvili et al Olson model Present data
0.01
H12 ¼
1E-3 1
10
100
1000
Energy (keV) Fig. 3. Total electron-capture cross section for K+–N2 collisions.
electron capture does not permit compression between the two measurements as far as the behaviour of excitation and charge transfer cross section as they should in principal show the same trend. However, measurements were made for the excitation function of the resonance emission line of 766.5 nm in collisions between potassium ions and N2 molecules [14] employing the same technique described in [8]. Their measurements [14] between 0.5 and 10 keV collisional energy for the KI (766.5 nm) emission line shows a clear maximum between 6 and 8 keV energy followed by a slow decreasing trend as it reaches 10 keV, while the same measurements in [8] shows that the emission line KI (766.5 nm) increases as the energy increases up to 6 keV and remain virtually constant as the collision energy increases to 10 keV. No explanation was offered regarding this difference in the 2001 publication [8]. On the other hand, considering our measured capture cross sections together with the data of [9,10] indicate a maximum between 20 and 50 keV collisional energy compared to the 6 keV maximum reported in [14]. Moreover, the excitation cross section reported by [14] for the K+–N2 processes is about a factor of three higher than that for K+–H2 from which they concluded that the excitation cross section is proportional to the energy defect of the colliding partners in the case of molecular targets. Yet this is in contrast to the data of [15–17] reported within [10], in which the reported capture cross section for K+–O2 (DE = 7.73 eV) is higher than that for K+–N2 (DE = 12.9 eV). While our present electron capture cross section of K+–N2 is about a factor of two lower than that for K+–H2, a behaviour that is confirmed by the data of [15–17] on K+ on N2 and O2 and reported within [10]. As a result, there is a need for further theoretical and experimental data regarding the above mentioned process in order to establish a reliable data for the K+–N2 collision system. However it is possible to evaluate the behaviour of the charge transfer cross section using the semiempirical model of Olson [18,19] for the system:
Kþ ð1 S0 Þ þ N2 ! K0 ð4s2 S1=2 Þ þ Nþ2 11:238 eV; The total single-electron-capture cross sections are calculated by the relation [18,19]:
r ¼ 4pR2c ½1 V 11 ðRc Þ=E0
Z 1
1
expðkxÞ½1 expðkxÞx3 dx
ð4Þ
V 022
where and are the first derivatives of the potentials V11 and V22 at Rc. The incident velocity is given by v0 and E0 is the incident energy. Rc is interpreted as the internuclear separation at which charge transfer occurs. Since, V11(Rc) is of the order of eV and the incident energy E0 of the order of keV, we can estimated ½1 V 11 ðRc Þ=E0 1. The coupling matrix element H12 was calculated through the relation:
2
cm )
V 011
ð3Þ
1 acR expð0:86R Þ 2
ð5Þ
where R ¼ 12 ðða þ cÞRc Þ. We used 12 a2 ¼ 15:58 eV as the effective ionization potential of the N2 target and 12 c2 ¼ 4:341 eV as the Kground-state electron affinity. H12 was found to be equal to 1.59 eV. While, Rc = 2.20a0, and jDV ; ðRc Þj ¼ 5:91 eV=a0 were fitted until the maximum cross section value corresponding to an energy Emax predicted by the Massey adiabatic model (evaluated using the energy defect |DE| as the only parameter) was obtained. The estimated electron transfer cross sections are shown in Fig. 3 as a solid line. The calculated r is seen to agree in behaviour with the present experimental data in the present energy range as well as with those of Gochitashvili et al. [8], Ogurtsov et al. [9], and Lo and Fite [10]. 4. Conclusions Absolute total electron transfer cross sections have been measured for the K+–N2 system, at impact energies between 1.0 and 3.5 keV. The charge transfer cross sections show a monotonic increasing behaviour as a function of the incident energy. Our present experimental data show continuity with the results of Ogurtsov et al. [9] which in turn show a reasonable overlap with the data reported by Lo and Fite [10] at higher energies. Our present electron capture cross sections as well as our previous data on K+–H2 increases as the energy defect decreases taking in agreement with the results of Lo and Fite [10] and Layton and Fite [17], while in disagreement with the data of Gochitashvili et al. [8]. The calculation of r employing the semi empirical model of Olson is seen to agree in behaviour with the present experimental data in the present energy range as well as well as with those of other groups. Agreement and disagreement with other groups points to the need for further theoretical and experimental data employing different methods regarding the above mentioned process in order to establish a reliable data for the K+–N2 collision system. Acknowledgments The authors are grateful to O. Flores, F. Castillo and José Rangel for technical assistance. This research was partially sponsored by DGAPA IN-109511 and CONACyT 128714. References [1] [2] [3] [4]
F.B. Alarcón, H. Martínez, B.E. Fuentes, F.B. Yousif, Phys. Scr. 88 (2013) 025304. F.B. Alarcón, H. Martínez, Nucl. Instrum. Meth. B 299 (2013) 29. R.E. Johnson, Icarus 143 (2000) 429. T.W. Hartquist, S.A.E.G. Falle, D.A. Williams, Astrophys. Space Sci. 288 (2003) 369. [5] A. Burrows, W.B. Hubbard, J.I. Lunine, J. Liebert, Rev. Mod. Phys. 73 (2001) 719. [6] D. Sudarsky, A. Burrows, P. Pinto, Astrophys. J. 538 (2000) 885. [7] F.M. Bieniosek, L.R. Prost, P.A. Seidl, A.W. Molvik, M. Kireeff Covo, Phys. Rev. Spec. Top. Accelerators Beam 10 (2007) 93201.
Please cite this article in press as: F.B. Alarcón et al., Single electron capture measurements in collisions of K+ on N2, Nucl. Instr. Meth. B (2014), http:// dx.doi.org/10.1016/j.nimb.2014.02.086
4 [8] [9] [10] [11]
F.B. Alarcón et al. / Nuclear Instruments and Methods in Physics Research B xxx (2014) xxx–xxx
M. Gochitashvili, B. Kikiani, R. Lomsadze, Hyperfine Interact. 132 (2001) 517. G.N. Ogurtsov, B.I. Kikiani, I.P. Flaks, Sov. Phys. 11 (1966) 362. H.H. Lo, W.L. Fite, Atomic Data 1 (1970) 305–328. F.B. Yousif, B.E. Fuentes, H. Martínez, J. Phys. B At. Mol. Opt. Phys. 43 (2010) 235206. [12] L.K. Johnson, R.S. Gao, C.L. Hakes, K.A. Smith, R.F. Stebbings, Phys. Rev. A 40 (1989) 4920. [13] M. Gochitashvili, B. Kikiani, R. Lomsadza, Hyperfine Interact. 132 (2001) 517.
[14] B.I. Kikiani, M.R. Gochitashvili, R.V. Kvizhinadze, V.A. Ankudinov, Zh. Eksp. Teor. Fiz. 87 (1984) 1906. [15] W.L. Fite, J.K. Layton, R.F. Stebbings, N.M. AFWL-TR-65-181, 1966 (Feb). [16] J.K. Layton et al., Phys. Rev. 161 (1967) 73. [17] J.K. Layton, W.L. Fite, N.M. AFWL-TR-67-2, 1967 (May). [18] R.E. Olson, F.T. Smith, E. Bauer, Appl. Opt. 10 (1971) 1848. [19] R.E. Olson, Phys. Rev. A 2 (1970) 121.
Please cite this article in press as: F.B. Alarcón et al., Single electron capture measurements in collisions of K+ on N2, Nucl. Instr. Meth. B (2014), http:// dx.doi.org/10.1016/j.nimb.2014.02.086